First of all, all the paradoxes of Zeno that I know have a common denominator: the relation between continuity and discreteness. So I assumed that the principled way of dealing with them is based on the same basic strategy, and from that standpoint there is no need at all to discuss each paradox separately.
If I am mistaken in this claim, I would be glad if you corrected me.

Second, you didn't answer me about the essence of the solution. I think a “technical” mathematical solution, even if successful, cannot replace an essential philosophical solution. That is true in this case too. One should also remember that in Zeno's own view there is a good solution to the paradoxes he raised.
I suspect that Alexandrovitz is basically just trying to bypass the problem (to deal in mathematical language with a problem from a different plane).

Third, Alexandrovitz's very attempt to bypass the paradox is, as I understand it, based on the same strategy Zeno himself uses. Its essence is an attempt to ground knowledge on a purely formal logical basis. What you call analyticity. It is an attempt to create an Aristotelian ideal of rationality whose price is emptying every claim of its content, and therefore Alexandrovitz's own claim as well.

I wrote my opinion about solutions via infinity to the arrow paradox in the article itself. But I can't answer a general question. One has to discuss a specific solution to a specific paradox.
By the way, the paradox of Achilles and the tortoise, for example, is not at all connected to the question of continuity and discreteness.

Which article? Zeno's arrow here on the site?

And another question: why is the paradox of Achilles not connected to the question of continuity? After all, there too the possibility of motion is blocked, according to Zeno, by the fact that space is divided in our mind into infinitely many discrete units. How is that different from the other two paradoxes that deal with exactly the same question?

Zeno's paradoxes are an ancient attempt (and Rabbi Michi is continuing it) to force logic onto physics.
The direct conclusion from Zeno's paradoxes is that physics doesn't give a damn about logic.
But ancient people with ancient thought were not (and many today still are not) capable of understanding this, and so the world remained stuck in the conception of egoistic logic for thousands of years.

Doron, yes.
The paradox of Achilles is not connected to the question of continuity but to convergent infinite series.

Decisor, isn't your use of “conclusions” itself a use of logic?

Student.
Logic has its honored place. And its place is in logical conversations between people.
Its place is not in forcing physical reality to operate according to it (or in other words, according to the logician's mindset).
Reality is not interested in whether someone is thinking logical thoughts and logical paradoxes.
Whoever believes that reality is compelled to operate according to his logic is like someone who believes that reality is compelled to operate according to certain rituals he performs—that is, by magic.

What does forcing have to do with it? Logic doesn't beat things with a big hammer; logic exposes what the person himself believes. You can always give up premises, but to hold the premises and not hold their conclusions is something I don't understand. Except for the law of non-contradiction, which operates even without any premises. Truthfully, I find it quite exciting to believe that things are not themselves, or to think that although every tree is flammable, there are trees that are not flammable. If reality does not obey the conclusion of a valid logical argument, that means there is an error somewhere in the premises; it has nothing to do with logic. Presumably you can't give an example.

It will take you a little time to understand that when the logician says, “Every tree is flammable,” he is not talking about trees in reality at all, but about trees in his feverish imagination.
The forcing happens when the logician thinks he is talking about trees in reality.
But it's all in his head. The forcing too. He is forcing his worldview to be extremely narrow. Typical of a common egoistic logician.

And what if the logician (the filthy egoist) says: every tree in reality is flammable, but there exist trees in reality that are not flammable.

Michi,

I'm dropping the main issue I asked about (we already had a long enough discussion about that in the comments on that column).

Instead, I'll address your claim that the paradox of Achilles deals with convergent infinite series.

Are you claiming that the essence of the paradox of Achilles is the discussion of those series (and not the problem of continuity and discreteness)? Is that the main point of this paradox?

If so, that's a claim I don't understand at all. It seems to me that the issue of the series is only a second layer, while the main thing is the question of continuity.

I don't see any point in exchanging declarations about it. My claim is that the paradox is solvable with the tools of the tenth century, without resorting to infinity. Sum the series of distances Achilles runs and the series of times, and you will see that this whole description describes (quite correctly) the first few seconds of the race. Achilles catches the tortoise exactly when those seconds have passed. That's all. There is no paradox here, and its solution has nothing whatsoever to do with the question of continuity.

Student.
What difference does it make what the logician says in terms of content? You can convert everything into symbols and then check their logical validity according to the rules of logic.
All his talk about trees and fire and columns of smoke is meant to mislead others into thinking he is dealing with reality.
He is merely dealing with basic and simple logical rules that human beings invented.

Michi,

For my sins, all I see here is a mathematical solution to a philosophical question (“sum the series of distances Achilles runs and the series of times, and you'll see”).
And after all, that is exactly what I objected to from the outset.
As best I understand it, even Zeno himself did not claim there was an unsolvable mathematical problem here.

I surrender.

^If* the night is confusing me